Global challenges Study Guide

Acceleration is the rate at which an object's velocity changes. This change can be in speed, direction, or both. Understanding the magnitude of acceleration in everyday situations helps us develop a practical sense of how forces affect motion. The standard unit for acceleration is metres per second squared (m/s²).

When estimating accelerations, it's useful to have some reference points. For example, the acceleration due to gravity on Earth is approximately 9.8 m/s², often rounded to 10 m/s². This means that an object falling freely will increase its speed by about 10 m/s every second. This magnitude provides a good upper bound for many everyday accelerations.

Consider a car accelerating from rest. A typical family car might take around 10 seconds to reach 100 km/h (approximately 28 m/s). This would give an average acceleration of about 2.8 m/s². A high-performance sports car might accelerate much faster, perhaps reaching 100 km/h in 3 seconds, resulting in an average acceleration of around 9 m/s². These values are often less than or comparable to the acceleration due to gravity.

Now consider deceleration. When a car brakes suddenly, it can experience significant negative acceleration. Emergency braking might produce a deceleration of 7-8 m/s². A person walking might experience very small accelerations, perhaps less than 1 m/s², when speeding up or slowing down. These examples illustrate a range of common acceleration magnitudes, from very small to those approaching the acceleration due to gravity.

For an object to maintain a stable orbit around a larger body, such as a satellite orbiting Earth or a planet orbiting the Sun, there must be a precise balance between the gravitational force pulling the orbiting object inwards and the tendency of the object to move in a straight line (due to inertia). This balance requires the object to move at a specific speed for a given orbital radius. The gravitational force between two masses decreases as the distance (radius) between them increases. Conversely, the gravitational force increases as the distance decreases.

Consider an object in a stable circular orbit. The gravitational force provides the centripetal force necessary to keep the object moving in a circle. If the orbital speed of the object increases while the radius remains constant, the centripetal force required to keep it in that orbit also increases. If the existing gravitational force is no longer sufficient to provide this increased centripetal force, the object will move outwards, increasing its orbital radius until a new stable orbit is established where the gravitational pull matches the new centripetal force requirement for that larger radius. In essence, a higher speed at the same radius would cause the object to 'fly off' at a tangent were the gravitational force not to adapt, or for the radius to adjust to increase the gravitational force or reduce the required centripetal force.

Conversely, if the orbital speed decreases while the radius remains constant, the required centripetal force decreases. In this scenario, the existing gravitational force would be stronger than the force needed to maintain the current orbit. This excess gravitational pull would cause the object to spiral inwards, decreasing its orbital radius until it finds a new, stable orbit closer to the central body, where a stronger gravitational force balances the reduced centripetal force requirement for that smaller radius. Therefore, for a stable orbit, an increase in speed necessitates an increase in orbital radius, while a decrease in speed necessitates a decrease in orbital radius.